few_shots: Example:
Problem/activity:
Task
Materials
One 10-frame per pair of students (see example below)
[IMG]
Counters, 10 per pair of students
Decks of number cards 0-5 (with 4 of each number) or two 0-5 dice
Setup
This activity is done in pairs. The students sit side by side with 10-frame and deck of cards or dice. If they have cards, the cards are shuffled and placed face down in front of them.
Action
Player 1 flips a card or rolls the die. They place that many counters on the 10-frame. Player 2 flips a card or rolls the die. They place that many more counters on the 10-frame next to the counters already on the ten frame. The students count the total together.
A recording sheet can be added when the students have been introduced to equations and number sentences. For those students who can handle higher numbers, a deck of 0-10 cards and two 10-frames can be used.
This game can also be played alone.


Mathematical concept/skill options: 
A. Write and interpret numerical expressions.
B. Generate and analyze patterns.
C. Analyze patterns and relationships.
D. Use properties of operations to generate equivalent expressions.
E. Use the four operations with whole numbers to solve problems.
F. Work with radicals and integer exponents.
G. Solve systems of equations.
H. Represent and solve problems involving multiplication and division.
I. Perform arithmetic operations on polynomials.
J. Understand the relationship between zeros and factors of polynomials.
K. Understand properties of multiplication and the relationship between multiplication and division.
L. Solve real-life and mathematical problems using numerical and algebraic expressions and equations.
M. Solve problems involving the four operations, and identify and explain patterns in arithmetic.
N. Use polynomial identities to solve problems.
O. Apply and extend previous understandings of arithmetic to algebraic expressions.
P. Rewrite rational expressions.
Q. Interpret the structure of expressions.
R. Add and subtract within 20.
S. Analyze and solve linear equations and pairs of simultaneous linear equations.
T. Represent and analyze quantitative relationships between dependent and independent variables.
U. Solve equations and inequalities in one variable.
V. Create equations that describe numbers or relationships
W. Reason about and solve one-variable equations and inequalities.
X. Represent and solve equations and inequalities graphically.
Y. Understand solving equations as a process of reasoning and explain the reasoning.
Z. Understand and apply properties of operations and the relationship between addition and subtraction.
AA. Gain familiarity with factors and multiples.
AB. Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.
AC. Work with addition and subtraction equations.
AD. Multiply and divide within 100.
AE. Work with equal groups of objects to gain foundations for multiplication.
AF. Represent and solve problems involving addition and subtraction.
AG. Write expressions in equivalent forms to solve problems.
AH. Understand the connections between proportional relationships, lines, and linear equations.


Thought: This task teaches students to understand addition as putting together counters, or adding to already placed counters.
Answer: AB

Now, assign the following problem or activity to one or more relevant mathematical concepts/skills it teaches.
shot_info: im_task_001477

K
options: Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.

Classify two-dimensional figures into categories based on their properties.

Solve real-world and mathematical problems involving area, surface area, and volume.

Define trigonometric ratios and solve problems involving right triangles.

Understand congruence in terms of rigid motions.

Explain volume formulas and use them to solve problems.

Experiment with transformations in the plane.

Translate between the geometric description and the equation for a conic section.

Understand and apply theorems about circles.

Analyze, compare, create, and compose shapes.

Prove geometric theorems.

Use coordinates to prove simple geometric theorems algebraically.

Graph points on the coordinate plane to solve real-world and mathematical problems.

Reason with shapes and their attributes.

Understand and apply the Pythagorean Theorem.

Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.

Draw and identify lines and angles, and classify shapes by properties of their lines and angles.

Make geometric constructions.

Visualize relationships between two-dimensional and three-dimensional objects.

Prove theorems involving similarity.

Apply geometric concepts in modeling situations.

Understand similarity in terms of similarity transformations.

Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres).

Apply trigonometry to general triangles.

Draw, construct, and describe geometrical figures and describe the relationships between them.

Understand congruence and similarity using physical models, transparencies, or geometry software.

Find arc lengths and areas of sectors of circles.
problem_activity: Optional activity
The goal of this activity is to verify, via angle calculations, that equilateral triangles (and hence) regular hexagons can be used to make regular tessellations of the plane. Students have encountered the equilateral triangle plane tessellations earlier in grade 8 when working on an isometric grid. In order to complete their investigation of regular tessellations of the plane, it remains to be shown that no other polygons work. This will be done in the next activity.
Students are required to reason abstractly and quantitatively (MP2) in this activity. Tracing paper indicates that six equilateral triangles can be put together sharing a single vertex. Showing that this is true for abstract equilateral triangles requires careful reasoning about angle measures.
Launch
In the previous task, equilateral triangles, squares, and hexagons appeared to make regular tessellations of the plane. Tell students that the goal of this activity is to use geometry to verify that they do.
Refer students to regular polygons printed in the previous activity for a visual representation of an equilateral triangle.
Representation: Internalize Comprehension.
Represent the same information through different modalities by using physical objects to represent abstract concepts. Some students may benefit by using virtual or concrete manipulatives (geogebra, tracing paper, or equilateral triangle cut-outs) to connect abstract concepts to concrete objects.
Supports accessibility for: Conceptual processing; Visual-spatial processing
Student Facing
What is the measure of each angle in an equilateral triangle? How do you know?
How many triangles can you fit together at one vertex? Explain why there is no space between the triangles.
Explain why you can continue the pattern of triangles to tessellate the plane.
How can you use your triangular tessellation of the plane to show that regular hexagons can be used to give a regular tessellation of the plane?
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Anticipated Misconceptions
Students may know that an equilateral triangle has 60-degree angles but may not be able to explain why. Consider prompting these students for the sum of the three angles in an equilateral triangle.
Students may not see a pattern of hexagons within the triangle tessellation. Consider asking these students what shape they get when they put 6 equilateral triangles together at a single vertex.
Activity Synthesis
Consider asking the following questions to lead the discussion of this activity:
“How did you find the angle measures in an equilateral triangle?” (The sum of the angles is 180 degrees, and they are all congruent so each is 60 degrees.)
“Why is there no space between six triangles meeting at a vertex?” (The angles total 360 degrees, which is a full circle.)
“How does your tessellation with triangles relate to hexagons?” (You can group the triangles meeting at certain vertices into hexagons, which tessellate the plane.)
“Are there other tessellations of the plane with triangles?” (Yes. You can make infinite rows of triangles that can be placed on top of one another—and displaced relative to one another.)
Consider showing students an isometric grid, used earlier in grade 8 for experimenting with transformations, and ask them how this relates to tessellations. (It shows a tessellation with equilateral triangles.)
Point out that this activity provides a mathematical justification for the “yes” in the table for triangles and hexagons.
Speaking: MLR8 Discussion Supports.
Use this routine to support whole-class discussion. After a response to one of the discussion questions is shared with the class, invite students to restate and/or revoice what they heard using mathematical language. Consider providing students time to restate what they hear to a partner, before selecting one or two students to share with the class. Ask the original speaker if their peer was accurately able to restate their thinking. This will provide more students with an opportunity to practice using language about tessellations.
Design Principle(s): Support sense-making


correct_option_index: 25